The objectivist account of cognition makes two inconsistent assumptions:
- The meaning of a sentence is a function that assigns the truth value to the sentence for each possible world. (This is a standard definition of meaning in objective is semantics.)
- The meaning of the parts cannot be changed without changing the meaning of the hole. (This is a requirement of any theory of meaning.)
To see the contradiction, notice the following:
Changing the meaning of the parts of the sentence should change the meaning of the sentence as a whole (by 2). This implies that the truth value of this sentence will also change for some possible world (by 1).
But, we can construct a sentence in which the meaning of its parts changes but its truth value remains the same in all possible worlds.
So, we have a contradiction.
Note: in unpacking the claim, Lakoff draws on an argument by Putnam (1981), which extends Lowenheim-Skolem's theorem from first-order logic to higher order-logic.